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WASHINGTON (CNN) -- The Supreme Court handed down two 5-4 decisions Monday on displaying the Ten Commandments, allowing an exhibit at the Texas capitol and barring others at two Kentucky courthouses.

In the ruling on the Kentucky cases, the majority determined the displays violated the Establishment Clause of the First Amendment that sets down the principle of separation of church and state.

The amendment states: "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof." The court has usually interpreted this to mean government actions must have a "secular purpose."

Only one of the nine justices voted differently in the two cases. Justice Stephen Breyer, considered a moderate liberal, voted against the displays in Kentucky but in favor of the one in Texas.

The key difference, Breyer said, was that the Kentucky displays stemmed from a governmental effort "substantially to promote religion," and the Texas display served a "mixed but primarily non-religious purpose."

Justice Sandra Day O'Connor, a moderate conservative, voted against the displays in both states and cast the swing vote in the Kentucky decision, which stopped short of forbidding such exhibits on all court or government property.

The decision allows the court some leeway to determine the appropriateness of displays on a case-by-case basis.

This was the first time the high court dealt with the issue of public displays of the Ten Commandments since 1980, when it ruled against them at schools in Kentucky.

Kentucky displays rejected

The Kentucky cases involved a dispute over two framed copies of the Ten Commandments displayed in two courthouses. The majority determined those exhibits went too far in promoting religious messages.

"The divisiveness of religion in current public life is inescapable," Justice David Souter wrote in the majority ruling, read from the bench.

"This is not time to deny the prudence of understanding the Establishment Clause to require the government to stay neutral on religious belief, which is reserved for the conscience of the individual."

Souter also pointed an image that hangs above the courtroom in the Supreme Court itself. It shows Moses carrying the Ten Commandments, but the tablets' text is not shown. Moses is alongside other historical figures such as Mohammed and Confucius.

"There is no risk that Moses would strike an observer as evidence that the national government was violating religious neutrality," Souter said.

Justices customarily read majority rulings from the bench, but Justice Antonin Scalia took the unusual step of reading a dissent from the bench.

Chief Justice William H. Rehnquist and Justices Anthony Kennedy and Clarence Thomas joined Scalia in the minority opinion on the Kentucky decision.

Scalia cited "the interest of the overwhelming majority of religious believers in being able to give God thanks and supplication as a people, and with respect to our national endeavors."

Texas monument donated in 1961

In the Texas case, a 6-foot-high granite Ten Commandments display was among nearly 40 monuments and historical markers spread across 22 acres in front of the capitol in Austin.

Rehnquist, reading the ruling in the Texas case, cited the complexity of deciding when and where Ten Commandments displays are permissible.

"No exact formula can dictate a resolution in fact-intensive cases such as this," Rehnquist read. "The determinative factor here, however, is that 40 years passed in which the monument's presence, legally speaking, went unchallenged.

"And the public visiting the capitol grounds is more likely to have considered the religious aspect of the tablets' message as part of what is a broader moral and historical message."

In a dissenting opinion, Souter wrote, "If neutrality in religion means something, any citizen should be able to visit [the capitol grounds] without having to confront religious expressions clearly meant to convey an official religious position."

The Fraternal Order of Eagles, a benevolent organization, donated the Texas monument to the state in 1961. The group gave thousands of such monoliths to towns around the country in the 1950s and '60s with support from filmmaker Cecil B. DeMille, director of the 1956 movie, "The Ten Commandments."

Thomas Van Orden, a suspended lawyer who described himself as a "religious pluralist," opposed the display and filed suit in 2002 after he became homeless, according to a New York Times report.

During arguments before the court in March, Van Orden's attorney, Erwin Chemerinsky, drew intense questioning from the justices over the limits of religious expression in government.

O'Connor asked, "If legislatures open their sessions, that the public can attend, with a prayer, why can't it allow monuments?"

White House backed displays

"The Supreme Court has made clear that Texas is a model for how governmental bodies across the country can constitutionally display religious symbols like the Ten Commandments," Abbott said.

"The Ten Commandments are a historically recognized system of law," Abbott said as he argued the case several months ago.

White House press secretary Scott McClellan said the White House had filed briefs in support of the displays in both states.

"The court took a different view than we had on the Kentucky case," he said. "We respect the court's decision."

The American Civil Liberties Union, which had challenged the Kentucky displays, said it "applauded" the decision on those displays, but legal director Steven Shapiro said the group disagreed with the Texas ruling.

The Union of Orthodox Jewish Congregations praised both decisions in a statement headlined, "Extreme positions rejected in favor of sensible approach of neutrality."

In March, lawyers representing the federal, state and county governments argued the 4,000 Ten Commandments displays in public courthouses and parks nationwide simply acknowledge the role belief in a higher authority has had in the development of the United States.

In the Kentucky cases, two counties posted copies of the King James version of the Ten Commandments on the walls of their courthouses.

The framed images were among other framed historical documents and symbols. All of the others were secular.

Mathew Staver, representing McCreary and Pulaski counties, argued in March that the "documents reflect American law and government."

Justice Ruth Bader Ginsburg said then that "these are not simple messages, like 'In God We Trust,' " on U.S. currency, she said.

"The Ten Commandments are a powerful statement of the covenant God made with his people," Ginsburg said.